Low envelope fluctuation OFDM waveform design under subcarrier constraints

In this paper, we propose an orthogonal frequency-division multiplexing (OFDM) weight design mechanism aimed at reducing envelope fluctuations under subcarrier constraints. In the time domain, a new metric is introduced and minimized to guide the OFDM waveform toward a constant-envelope structure. In the frequency domain, the design allows a subset of subcarrier weights to be pre-assigned and imposes upper bounds on the magnitudes of the remaining subcarrier weights. Specifically, we formulate and solve an optimization problem that minimizes the variance of the envelope distribution, subject to subcarrier constraints and a fixed total energy budget. This leads to a non-convex optimization problem. By relaxing certain constraints-specifically, the upper-bound constraints on weight magnitudes-and subsequently reintroducing them, we transform the original non-convex problem into an unconstrained maximization over a unimodular complex vector and develop an iterative solution approach that converges to a local optimum. In addition, the effect of the initial point selection on the resulting weights is analyzed, which motivates a heuristic strategy for roughly controlling weight magnitudes. Numerical results demonstrate that the proposed method effectively suppresses envelope fluctuations while satisfying subcarrier constraints. Compared to existing methods, the proposed mechanism achieves higher computational efficiency and a better approximation to a constant-envelope signal.